It is proposed to develop efficient computational algorithms which will permit comprehensive mathematical modelling of the kidney. At present we have models with one or two solutes and pressures; this essentially means that we can solve mass balance equations for a maximum of two hundred spacial compartments in the kidney. Extension of the efficiency of our algorithms will permit us to handle more realistic models having considerable spacial complexity, several solutes and/or pressures. Partitioning, projections, high order integration methods and structural information about the kidney will be utilized to develop algorithms for the efficient solution of the nonlinear systems describing the models. Practical algorithms and the relevant theory will also be developed for the estimation of the parameters of the kidney from the available experimental data.